Stability of positive nonlinear systems

Abstract

The stability of time-invariant positive nonlinear systems is addressed. Necessary conditions for the stability of positive time-invariant continuous-time and discrete-time nonlinear systems are established. It is shown that the positive nonlinear systems are asymptotically stable only if the corresponding positive linear systems are asymptotically stable. Considerations are illustrated by numerical examples and simulations are performed in Matlab-Simulink environment.